Finite Group Databasebeta

← #44529480

Subgroups — #44529480

Order 31168.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#29510237C211yesmaximal, characteristic, complemented
2#29510161C211yesmaximal, characteristic, complemented
3#29510159C211yesmaximal, characteristic, complemented
4#29510158C211yesmaximal, characteristic, complemented
5#29510156C211yesmaximal, characteristic, complemented
6C2×C487⋊C16C211yesmaximal, characteristic, complemented
7#135×C487C211yesmaximal, characteristic, complemented
8#21441261—21no—
9Dic1948C2211yescharacteristic
10#21441250—21no—
11D3896C2211yescharacteristic
12C487⋊C16C2211yescharacteristic
13C487⋊C16C2211yescharacteristic
14#41×C487—21no—
15Q16×C487C2211yescharacteristic
16SD16×C487—21no—
17D8×C487C2211yescharacteristic
18C2×C8×C487C2211yescharacteristic
19Dic974—21no—
20D1948—21no—
21C22⋊D487—41no—
22C4×D487—41no—
23Q8×C487—21no—
24D4×C487—21no—
25D4×C487—41no—
26C2×C4×C487—41no—
27C2×C4×C487D411yescharacteristic
28C8×C487D411yescharacteristic
29C8×C487C2311yescharacteristic
30C22×C487—41no—
31C22×C487D811yescharacteristic
32C2×D487—41no—
33C4×C487—41no—
34C4×C487D811yescharacteristic
35C4×C487C2×D411yescharacteristic
36Dic487—41no—
37C2×C487—21no—
38C2×C487—81no—
39C2×C487C2×D811yescharacteristic
40D487—81no—
41C487#50811yescharacteristic, complemented, Sylow
42#508—4871nomaximal, Sylow
43#135—4871no—
44#135D48711yescharacteristic, complemented
45Q32—4871no—
46SD32—4871no—
47SD32—4871no—
48D16—4871no—
49C2×C16—4871no—
50#41—21no—
51#41—9741no—
52Q16—4871no—
53Q16C2×D48711yescharacteristic
54SD16—21no—
55SD16—9741no—
56D8—4871no—
57D8C2×D48711yescharacteristic
58C2×C8C2×D48711yescharacteristic
59C16—4871no—
60C16—4871no—
61Q8—21no—
62Q8—9741no—
63D4—21no—
64D4—41no—
65D4—19481no—
66D4—9741no—
67C2×C4—41no—
68C2×C4—19481no—
69C2×C4C22⋊D48711yescharacteristic
70C8C22⋊D48711yescharacteristic
71C8C22×D48711yescharacteristic
72C22—41no—
73C22—19481no—
74C22#2144124611yescharacteristic
75C4—41no—
76C4—19481no—
77C4#2144124611yescharacteristic
78C4C2×C22⋊D48711yescharacteristic
79C2—21no—
80C2—81no—
81C2—38961no—
82C2C2×#2144124611yescharacteristic
subgroupG/H
centerC4#21441246
commutator, cosocleC8×C487C23
FrattiniC8C22×D487
Fitting#135×C487C2
socleC2×C487C2×D8
hypercenter#135D487
hypocenterC487#508
LCSG ▷ C8×C487 ▷ C4×C487 ▷ C2×C487 ▷ C487
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #29510237C2semidirect
2. #29510161C2semidirect
3. #29510159C2semidirect
4. #29510158C2semidirect
5. #29510156C2semidirect
6. C2×C487⋊C16C2semidirect
7. #135×C487C2semidirect
41. C487#508semidirect
44. #135D487semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#295102372
#295101612
#295101592
#295101582
#295101562
C2×C487⋊C162
#135×C4872
#508487